Translating solutions of the nonparametric mean curvature flow with nonzero Neumann boundary data in product manifold $M^n\times \mathbb{R}$

Abstract

In this paper, we can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary data in a prescribed product manifold $M^n\times \mathbb{R}$, where $M^n$ is an $n$-dimensional ($n\ge 2$) complete Riemannian manifold with nonnegative Ricci curvature, and $\mathbb{R}$ is the Euclidean $1$-space.

22 pages. A related paper [Y. Gao, J. Mao, C.-L. Song, Existence and uniqueness of solutions to the constant mean curvature equation with nonzero Neumann boundary data in product manifold $M^n\times \mathbb{R}$, preprint.] will be put on arXiv very soon. Comments are welcome. Several revisions have been made in Section 1 of v1

References in corpus (3)

• The half-space property and entire positive minimal graphs in M x R
• Periodic constant mean curvature surfaces in H^2 x R
• The Dirichlet Problem for the Minimal Surface System in Arbitrary Codimension

Cited by in corpus (1)

• Existence and uniqueness of solutions to the constant mean curvature equation with nonzero Neumann boundary data in product manifold $M^n\times \mathbb{R}$